Craig Kimbrel notched his 31st save of the season with a scoreless ninth inning against the Marlins on Saturday.

Advice: Kimbrel took the mound with the Padres holding onto a 5-3 lead. He retired all three batters he faced and ended the game with a strikeout of J.T. Realmuto. At various times over the last week, the all-world closer was attached to multiple trade rumors. None of them came to fruition, though, and Kimbrel should close out the season in San Diego. He holds a 2.76 ERA and 58/15 K/BB ratio in 42 1/3 innings while going 31-for-33 in save chances.

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Evan Drellich was told by an Astros source that the "ship has sailed" on Craig Kimbrel.

Advice: The Yankees also aren't getting Kimbrel, so it appears the reliever is probably staying put. The Astros could still acquire Aroldis Chapman to bolster their bullpen.

Advice: ESPN's Buster Olney adds that the two sides haven't had any talks on Friday, so it appears that ship might have sailed. The Yankees are still in the market for a reliever, though, with Carter Capps and possibly Aroldis Chapman piquing their interest.

ESPN's Buster Olney reports that the Yankees "keep hammering away" at a trade for Craig Kimbrel.

Advice: The Astros and Red Sox have also talked to the Padres about Kimbrel, but it appears the Yankees might be the frontrunner here. CBS Sports' Jon Heyman hears that the Padres have sought shortstop prospect Jorge Mateo in a deal for Kimbrel. The Yanks had been viewing him as untouchable but might be altering that position. Acquiring Kimbrel would give New York a dynamic trio at the back-end of the bullpen, with Dellin Betances and Andrew Miller serving in setup roles.

Joel Sherman of the New York Post reports that rival executives view the Yankees as the favorite to land Craig Kimbrel from the Padres.

Advice: The Yankees are in the market for both rotation and bullpen help. Kimbrel would join Dellin Betances and Andrew Miller to form perhaps the finest late-inning trio in all of baseball. The Padres are currently listening to offers on many of their players and expected to make big moves before Friday's deadline.

ESPN's Jerry Crasnick reports that the Astros are "monitoring the relief market" and have discussed Craig Kimbrel, Joaquin Benoit and Francisco Rodriguez.

Advice: It doesn't sound like they're close to anything, but it appears the Astros are interested in adding to what has been a very good bullpen. Of the three aforementioned relievers, only Benoit could be a free agent after the season (he has an $8 million club option for 2016).

CBS Sports' Jon Heyman reports that Craig Kimbrel's name "has at least surfaced" in the Padres' trade talks with the Yankees.

Advice: As Heyman notes, it's hard to see a fit given that the Yankees already have a dynamic 1-2 punch with Dellin Betances and Andrew Miller at the back-end of their bullpen. They would seem likelier to add one of the starters the Padres are shopping, with Heyman saying the Bombers "are investigating most starters and relievers on the market."

FOX Sports' Ken Rosenthal reports that the Nationals are "hottest" on Craig Kimbrel.

Advice: The Nats have also been linked to Aroldis Chapman, as they appear determined to land an elite closer despite Drew Storen's fine season. Rosenthal adds that the Padres asked for Trea Turner (who they traded to Washington over the winter) from the Nationals in trade talks but were told it wouldn't happen.

According to CBS Sports' Jon Heyman, the Nationals and Blue Jays are among the teams looking into acquiring Padres closer Craig Kimbrel.

Advice: Washington and Toronto have also been linked to Jonathan Papelbon and Aroldis Chapman. It's a market flush with late-inning relief help, with Tyler Clippard, Francisco Rodriguez, and Jim Johnson also being dangled publicly ahead of the July 31 trade deadline. Kimbrel has been his usual dominant self after a shaky first few months in a Padres uniform, boasting a 2.75 ERA and 55/15 K/BB ratio in 39 1/3 total innings along with 29 saves.